My research interest is Number Theory and Arithmetic Geometry, and their applications to cryptography and coding theory. Currently I am interested in the following subjects:

(1)Fontaine theory of p-adic representations and (φ,Γ)-modules, and its connection to Iwasawa theory.

(2)Theory of elliptic curves and its application in cryptography.

(3)Class groups and class numbers of number fields and function fields, Cohen-Lenstra Heuristics.

l Preprints (in alphabet order if not stated otherwise):

1. Jean-Marc Fontaine and -, Theory of p-adic Galois representations, new version, 2022.

2. Xianhong Xie, - and Ming Mao, Vectorial bent functions and Linear Codes from Quadratic Forms, preprint, 2020.

3. Jianing Li, Songsong Li and -, Factorization of Hilbert class polynomials over prime fields, preprint, 2021. arXiv:2108.00168

4. Xianhong Xie and -*, On vectorial functions with maximal number of bent components, preprint, 2022.

5. Sen Wang, -* and Xianhong Xie, New Classes of Optimal and Distance Optimal Two or Three-weight Codes, preprint, 2022.

6. – and Jianfeng Xie, Unboundedness of Tate-Shafarevich groups in fixed cyclic extensions, preprint, 2022.

l Publications (in alphabet order if not stated otherwise):

1. - and Jianfeng Xie, The growth of Tate-Shafarevich groups in cyclic extensions, Compositio Math. \textbf{158} (2022), 2014–2032.

2. -，Sen Wang and Xianhong Xie, Almost balanced and uncorrelated quaternary sequence pairs of even length. JUSTC, 2022, 52(3): 4.

3. Xianhong Xie, -, Honggang Hu and Ming Mao, Construction of three classes of Strictly Optimal Frequency-Hopping Sequence Sets, , Advances in Mathematics of Communications 2022. doi: 10.3934/amc.2022024.

4. Jianing Li， -, Yue Xu, On abelian 2-ramification torsion modules of quadratic fields, Sci. China Math., 2022, doi: 10.1007/s11425-021-1946-0.

5. Bei Wang, Songsong Li, - and Honggang Hu. Ready-Made Short Basis for GLV+GLS on High Degree Twisted Curves, AIMS Mathematics, 2022, 7(1): 306-314. doi: 10.3934/math.2022021.

6. Bei Wang, Xianhong Xie, Songsong Li, - and Honggang Hu, General 4-GLV Lattice Reduction Algorithms, Proceedings of 2021 17th International Conference on Computational Intelligence and Security (CIS’2021), 430-434, 2021.

7. Jianing Li, -, Yue Xu, 阿贝尔p 分歧扭子群和新Cohen-Lenstra 猜想, (Abelian p-ramification groups and new Cohen-Lenstra heuristics), Sci Sin Math. 51(2021), No. 10, 1635-1654.

8. Bei Wang, -， Songsong Li and Honggang Hu: A New Twofold Cornacchia-Type Algorithm and Its Applications, Advances in Mathematics of Communications 2021, doi:10.3934/amc.2021026.

9. Jianing Li, -, Yue Xu and Shenxing Zhang, l-Class groups of fields in Kummer towers, Publ. Mat. 66 (2022), 235–267.
10. Songsong Li, - and Zheng Xu, Endomorphism rings of supersingular elliptic curves over F_p,，Finite Fields Appl. 62(2020), February 2020, 101619.
11. Songsong Li, - and Zheng Xu, Neighborhood of the supersingular elliptic curve isogeny graph at j=0 and 1728, Finite Fields Appl. 61(2020), January 2020, 101600.
12. - and Zheng Xu, Loops of isogeny graphs of supersingular elliptic curves at j=0, Finite Fields Appl. 58 (2019), 174-176. (local)
13. – and Xianhong Xie, Linear complexity of generalized cyclotomic sequences of period 2p^m, Des. Codes Cryptogr. 87 (2019), no. 11, 2585-2596. (local)
14. Yang Liu and -, On binary quadratic forms modulo n, Commun. Math. Stat. 7 (2019), no. 1, 61-67. (local)
15. Songsong Li and -, Counting the solutions of λ₁x₁^k`+… λ_t x_t^kt≡ c mod n, J. Number Theory 187(2018), 41-65. (local)
16. Bei Wang, - and Honggang Hu, Efficient Pairing Computation on Twisted Weierstrass Curves, Chinese J. Electronics 27(2018), 739-745.(local)
17. - and Jinbang Yang, On a conjecture of Wan about limiting Newton polygons, Finite Fields Appl. 41(2016), 64-71. (local)
18. - and Shenxing Zhang, Newton polygons of L-functions of polynomials x^d+ax^d-1^with p≡-1 mod d, Finite Fields Appl. 37(2016), 285-294. (local)
19. - and Shenxing Zhang, Birch's lemma over global function fields, Proc. Amer. Math. Soc. 145(2017), 577-584.
20. – and Jinbang Yang, Newton Polygons of L functions of polynomials x^d+ax, J. Number Theory 160(2016), 478-491.
21. – and Shenxing Zhang, On second 2-descent and non-congruent numbers, Acta Arith. 170 (2015), 343-360. Errata, Acta Arith. 202 (2022), 203-203.
22. – and Zhe Zhang, Hilbert genus fields of real biquadratic fields, Ramanujan J. 37(2015) 345-363.
23. - and Zhe Zhang, Hilbert genus fields of biquadratic fields, Sci. China Math. 57, No. 10(2014), 2111--2122.
24. - and Jinbang Yang, On the cohomology of semi-stable p-adic Galois representations, C. R. Math. Acad. Sci. Paris Vol. 352(2014), 557--561.
25. – and Shenxing Zhang, On non-congruent numbers with 1 modulo 4 prime factors, Sci. China Math. 57, No. 3(2014), 649--658.
26. -, Lectures on p-adic zeta functions and (φ,Γ)-modules, in Number Theory and Related Area, pp. 85-147, 2013.
27. -, F. Xu, C. Xing and P. Zhang, Number Theory and Related Area, editor, Advanced Lecture in Mathematics, Vol.27, Higher Education Press and International Press, 2013.
28. Yiwen Ding and -, A simple proof of Dieudonné-Manin classification Theorem, Acta. Math. Sin. (Engl. Ser.) Vol. 28, No. 8 (2012), 1553--1558.
29. - and Hang Xue, Class numbers of Cyclic 2-extensions and Gross conjecture over Q, Sci. China Math. Vol. 53, No. 9 (2010), 2447--2462.
30. Kumar Murty and -, The growth of Selmer ranks of an abelian variety with complex multiplication, Pure and Appl. Math. Quarterly 2, No. 2(2006), 539-555.
31. -, The Gross conjecture over rational function fields, Science in China, Ser. A. Mathematics 48, No. 12 (2005), 1609-1617.
32. -, The universal Kolyvagin recursion implies Kolyvagin recursion, Acta. Math. Sinica, English Ser. 23, No.7 (2007), 1163-1172.
33. On the universal norm distribution, J. Ramanujan Math. Soc. 17,
    No. 4 (2002), 287--311.
34. Greg W. Anderson and -, A note on the cyclotomic Euler systems and the double complex method, Can. J. Math. 55, No.4(2003), 673--692
35. -, The universal norm distribution and Sinnott's index formula, PAMS 130(2002), No. 8, 2203-2213.
36. -, The group cohomology of universal ordinary distribution, Crelle 537(2001), 1--32.
37. My thesis Group cohomology of the universal ordinary distribution and its applications, University of Minnesota, advisor: Greg William Anderson. 2000.
38. - and Fei Xu, Riemann-Hurwitz formula in Basic Zs-extensions, Acta Arith.LXXXI.1 (1997), 1--10.
    
    

l Other Writings　

1. Galois和Kummer对于代数数论发展的贡献, 厦门大学东南数学中心短期课程，2020年8月，中文版，英文版

2. The China Legacy of Jean-Marc Fontaine, la Gazette des Mathématiciens No. 162，Octobre 2019, 15-17.

3. (冯克勤, 欧阳毅) 中法数论代数几何合作, 《清华数学90年》，清华大学, 2017.

4. 仿佛来自虚空---亚历山大·格洛腾迪克的生平故事, 译自 Allyn Jackson的著名文章Comme Appelé du Néant, As If Summoned from the Void: The Life of Alexandre Grothendieck, Part I, Notices AMS, Vol 51, No. 9; Part II, Notices AMS, Vol 51, No. 10, 发表于《数学译林》.

5. 黎曼假设有关的数学巨匠和数学进展. 见《代数学III：代数学进阶》数字课程网站 (http://abook.hep.com.cn/1251847).

6. 艾米·诺特小传. 同上.

7. 二次曲线和p进数. 同上.

8. Inverse limits and Galois Theory. 同上.

9. Introduction to Iwasawa theory.

10.(葛力明, 欧阳毅, 田野, 邢朝平, 徐飞) 冯克勤先生简介, SCIENTIA SINICA Mathematica, 2021.

l The followings are some documents which should be useful to some of you:

• Pierre Colmez's Tsinghua lecture notes (Fall 2004) on p-adic L-functions and Fontaine rings.
• Luc Illusie's course notes (Feburary-June 2004) on algebraic geometry.
• Emmanuel Ullmo's course notes (Fall 2005) on modular forms and modular curves.

l 近日有多名学生咨询研究生导师的事情，鉴于研究生导师肩负的巨大责任，特此声明：本人不接收没有深入了解的同学作为研究生，特别地对于科大本科生，本人原则上只接收指导过大研计划和/或毕业设计的同学。（当然，如果你没有看到这句话，说明你对于了解我其实并没有兴趣，那就相忘于江湖吧）